What's the probability that two stars collide when galaxies collide? [with equations!]

[@Jaxen90841]

If the Sun were a grain of sand, the Alpha Centauri trinary system would be three more grains of sand about four miles away. Galaxies are that empty.

[@XavierMathewsEntertainment]

This was a really good way of explaining it.

[@paavobergmann4920]

*gulp* ok. Thanks. You get some sense of it playing "Elite Dangerous" when it takes you like forever to get to the planets of the second star of a binary system, and then you look at the speedometer and realize you´ve been going at like 200c for like 15 minutes and those little points of light were not moving a bit in your view..... Another good representation was the video of the other guy, who built a model of the sun and proxima Centauri by laying down a golfball somewhere in England, and then showing a time-lapse of his dashcam while he drove to Spain, where the other golfball was placed....

[@ibenzawla]

Finally a explanation for anyone to understand.

[@ximalas]

And our farthest pieces of technology has hardly left the Solar system, even though they have been on their merry way for the past 40+ years.

[@OrcinusDrake]

@Tony Samson oof that is far too many significant figures lol

[@alexliger1893]

This was as close to re-using pV=Nrt as I ever came since graduating college. Thank you. Btw, your enthusiasm is contagious!!

[@PauxloE]

So the number at 9:04 is the expected number of stars being hit by the Sun during the merger (which is approximately the probability of hitting exactly one of them, as the probability of hitting more than one is very tiny). Dividing by the number of stars in Andromeda (9:35) gives the *probability of the Sun hitting a specific one of those* (not the probability of hitting any of them). If you multiply it by the number of stars in the Milky Way, you get the expected number of collisions for all MW stars, which comes out to a nice 400 · 10^9 × 1.1 × 10^-9 = 440. Without even doing this binomial formula, this indicates to me that the probability of at least one collision is almost one. If we want to use the binomial formula at 11:13 with p = 1.1 ×10^-21, we actually need n = number of stars in MW × number of stars in Andromeda = 400·10^9 × 10^12 = 4 × 10^21. Wolfram Alpha fails to calculate exact percentages for one or 0 hits (overflow/underflow), but it can tell us that the mean (expected value) is 440 (which is what I got above too): www.wolframalpha.com/input/?i=binomial+distribution+n+%3D+400·10%5E9+×+10%5E12,+p+%3D+1.1+×10%5E-21

[@tatjanagobold2810]

More math videos please! They make astronomy and astrophysics much more understandable and fun :)

[@gregvaughan8412]

t. gobold Look up David Butler. Fantastic videos kzbin.info/www/bejne/q4fbo6aAatGNorM

[@PetraKann]

....less understandable imo. Remember Mathematics is a discipline of the Arts - a neurotic abstract sub branch of Philosophy akin to a fundamentalist religious sect

[@juanvia8394]

Thank you for the math. We like to be treated like thinking beings.

[@K1lostream]

Juan Via - Speak for yourself - Becky found my level at the end when she was doing sound effects of the musical overture to a galaxy merger!

[@DarkAngel71180]

K1lostream listen to the math one part at a time to understand it better, that's what I had to do. And I had to repeat it. I'm not great at math.

[@TheTeufelhunden68]

@@DarkAngel71180 Sure you are. You probably don't use math, at least higher math, on a daily basis.There are loads of books available to help you hone your skills. Don't sell yourself short. And, hey. so you backed the episode up a few times. You still got it.

[@jessstuart7495]

r = particle radius R = cylindrical region radius L = length of cylindrical region rho = stellar density P = probability of single star collides with another star The probability of collision becomes just a ratio of cross-section areas times the number of stars in the region (number of stars = density * volume). P = pi*(2*r)^2/(pi*R^2) * rho * (pi*R^2*L) simplify... P = 4*pi*r^2*L*rho Multiply this by the number of stars in our galaxy to estimate the average number of particle collisions. Then use this to define a Poisson distribution using the "average" and use this distribution of calculate the probabilities of 0, 1, 2 , 3... collisions.

[@jwarmstrong]

@@jessstuart7495 What are the numbers of collisions if the black holes collide on first pass in the most dense region of stars.

[@Urroner]

My dad was a high school teacher and principal. He was s great teacher zinc the kids loved him. He told me the “secret” to his success and it wasn’t much of s secret, the kids need to enjoy the class, to have fun, and the teacher needs to enjoy teaching them. Dr. Becky makes her lessons fun by her expressions, adding little tidbits to her classes, and showing in spades her enthusiasm for the subject. She could easily overwhelm us with her intelligence and her knowledge, but she had never in any of the videos that I have watch, had ever done that. Thank you Dr. Becky.

[@theCodyReeder]

Something I’ve always wondered is what are the odds of a high velocity object launched from earths surface towards a random direction in the sky ever actually hitting anything?

[@DrBecky]

I put together something kind of similar once. If you were launched at the zenith at the moment of your birth at light speed, where would your nearest star be now? The odds of hitting anything in a random direction is harder, probably more likely to hit space junk in orbit around the Earth than something in the solar system or beyond

[@Jaxen90841]

@@DrBecky another KZbinr, David Butler, conjectured how long it would take one of our Voyager spacecraft to reach a point where it could look back and see our Milky Way as a whole. He calculated that it would take about 500 million years to reach such a point. Our own solar system would be less than one pixel in its frame. What he didn't think of is, at our current speed that we are circling the galaxy, we will circle closer to that point sooner than Voyager will.

[@drhextube]

@@Jaxen90841 But surely, Voyager has nowhere near galaxy escape velocity. It will keep orbiting the milky way centre.

[@yahccs1]

​@@DrBecky A nice idea... perhaps a part of us is out there among the stars - or a message would be if a "Baby [name] is born!" message was 'beamed out' into space at that point. I suppose I could look up what stars were overhead at the time and location of my birth. I just know that hospital is no longer there now. Somewhere around 51 North on a certain Monday in February... PS I wonder what the probability is of the Lucy mission probe (or any other solar system probes) hitting an unknown asteroid on its trajectory. I hope it would detect such an object first and send back pictures and data from it before it says a quick 'goodbye'!

[@bluenote36]

@@DrBecky I was wondering about your simplifying assumptions. What if you add in the fact that the galaxies merging are extremely unlikely to be coming in with their disk axes parallel. How does that change things since you actually have two cylinders at varying angles crossing at some point. Also, what about the affect of the gas in the two galaxies which I believe will eventually fall into the center of mass of the colliding system and then affect the gravitational pull on the stars.in the two galaxies. Finally when you take into account that most mergers of star-like objects we see are objects spiraling into each other (possibly because of the gravitational affect of the gas?), how does taking gravitational affects influence the likelihood of merger?

[@olafnielsen8389]

What about the disruption of planetary or sub-planetary orbits from a passing star, both of which could be catastrophic locally. Or the effect of a single star system capturing another star to become a binary system.

[@pogtuber5146]

This seems almost less likely. Proxima Cenaturi has no affect on our solar system, and the distance between our system and the Centauri system is so vast than any systems of our size would not likely change anything about our system.

[@Theodore042]

The difference in relative speed between two stars would probably make it "impossible" for a near miss to become a binary system. And the effect of gravity falls off really fast (on a solar scale anyway) but its hard to imagine a sun-sized star sailing past Pluto and not messing with the inner planets at least a little...

[@pogtuber5146]

@@Theodore042 Yes exactly, but the chance of a sun getting as close to pluto as it is to our current sun is again astronomically small, considering again how much more likely it is that a random star just flies through the vast space between us and Centauri instead, I think.

[@scollyb]

The solar system is about 10,000 times the diameter of the sun, which gives a cross sectional area of 100 million times (I am ignoring geometry, in reality to the angle of the disk will have a major impact but a star passing within 40 AU or so of the Sun will have some effect). So with wild assumptions you up to about a 4% chance that one star passes close enough to another to have an impact on the planets. Capture is going to very unlikely, in a purely gravitational two body problem capture is impossible. You either need non gravitational forces to remove energy or a 3+ body system in very specific geometries.

[@seraphina985]

@@scollyb A potential period of increased impact events due to the perturbation of the oort cloud is probably somewhat more likely still something like that could potentially trigger a era similar to the late heavy bombardment to happen again due to interactions with large numbers of new long period comets having been deflected onto very elliptical orbits. Course heavy is relative here as you are still talking about a potential anomaly in the frequency of impact events on a geological timescale, besides which if humans are even still around in several billion years the technologies available to prevent comets striking things that we would prefer they didn't are likely to far exceed those available currently laser propulsion stations for example would be very effective for sublimating volatile ices of a comet to change it's trajectory for example.

[@charles-y2z6c]

I will be sleeping better knowing the odds, i was really worried about it.

[@GimmieTheGaff]

What you share and teach means so much to me. I’m old but I still stare at the night sky with awe, and now I have the delight of you and all the other brilliant young folk telling me the how and why online. Bless you.

[@ullo-ragnartelliskivi4639]

your exitement is catchy. its so nice to see you light up with the word "math". keep up the good work !

[@CoolBeansGG]

If i had a teacher like you explaining me math i wouldn't struggle as i did, i understood you perfectly and English isn't even my first language. Great presentation and explanation ! I really enjoy watching your videos, universe never cease to amaze me and is one of my biggest amater passions, i am looking forward of future uploads, sending regards from EU / Slovenia ( I think it would be great to hear your thoughts about great attractor, i know you scientists hate to speculate and prefer facts,but still..)

[@BIGV1N]

This really puts the immense distances within galaxies into perspective for me! Happy Wednesday Dr. Becky, hope you're having a beautiful week!

[@rationalmartian]

That is a great point, that I feel should be underlines MUCH more often. Most people seriously underestimate the sizes and distances involved when talking about space. Having obtained the lions share of what they know from TV, a video, odd documentary and even Sci Fi. The animations or models can NEVER actually show anything remotely to scale. Something has to give. The distance are just too great. It impossible to show two different bodies in space to scale. One of the objects would be virtually impossible to see. It is just about possible with the two inner planets, Mercury and Venus and the Sun, by the time it gets to us, the Sun is becoming small, by Mars even harder to distinguish scale, and after that the Sun becomes almost a spot of light. Attempting to actually explain and picture or grasp the distances involved takes a little time becoming familiar with the vast, immense, mind boggling distances involved. Even with the closest stars. Galactic sizes are something another few orders of magnitude larger, galactic clusters is yet another leap in having ones mind boggled. Larger than that and one must take the effort to try, but even a slight tentative grasp of the utter immense hugeness involved becomes difficult, almost impossible to envisage in any kind of realistic way. Suffice to say, our Universe is a damn voluminous space.

[@markfox1545]

V Smart - you're not v smart at all to put YOUR instead of YOU'RE. Simpleton.

[@BIGV1N]

@@markfox1545 your write, they're should have ben an apostrophe in their ;)

[@TheRealMirCat]

What's the probability for getting swallowed up by Andromeda's supermassive black-hole? And when/should the two supermassive black-holes merge, what will it's gravity wave be like?

[@ffggddss]

This could lead to another calculation - given the fraction of galaxies that have central BH's, and the rate at which galaxies are merging, and some assumptions about the sizes of those BH's, what rate of BH-merger detections from such mergers can we expect to see in our grav-wave detectors? I don't have numbers for any of the inputs for this calculation; I bet Dr. Becky has them, though... Fred

[@WadcaWymiaru]

There is two of them...

[@judsonkr]

Well if Andromeda's supermassive black-hole has not yet swallowed up Andromeda then I think the Milky Way is safe. At least for the foreseeable future.

[@RodelIturalde]

It is like very hard to hit a black hole.

[@EASYTIGER10]

This reminds me of "the chair leg paradox" which I thought up when I was about 10: "The % of the area of the dining room floor taken up by the table and chair legs is very small. So why does my radio controlled buggy keep hitting them?"

[@nickv4073]

Your dining room floor is only two dimensional and only 10x20 ft on average. Not very big is it.

[@tehbonehead]

The same can be said for toes in the dark...

[@olly5764]

Always worth hanging on right to the end to hear Becky sing!

[@EebstertheGreat]

When you take into account the various effects you mentioned at the end of the video, the probability of a collision may still be very small, but it might be large enough for us to potentially observe the aftermath of collisions if we knew what to look for and could check enough galaxies.

[@joetaylor486]

Ace vid, Dr Becky! So it's basically a slightly massive open space passing through another slightly massive open space. Loved the verbalised sound track!

[@chuckinwyoming8526]

Dr. Becky, you are a real star doing a smashing job describing a highly improbable Star smashup!

[@TheTeufelhunden68]

Not improbable at all. According to the math, it WILL happen. The probability of it happening to any given star is low, i.e., our own sun.

[@Jenab7]

If two bodies having total mass M (i.e., M=M₁+M₂) are initially at rest and separated by a distance d, the time to fall until the separation is r, such that r

[@barefootalien]

I see two problems with this calculation, unless I'm missing something... One is: why do you use the volume density of the stars? The way you're simplifying this as a cross-sectional area over a velocity and time, shouldn't you use the cross-sectional area-density of the stars? The other is: why did you divide by the number of stars at the end? Isn't the 1.1E-9 the probability that the sun will impact any star in Andromeda? Therefore, why wouldn't you multiply by the number of stars in the Milky Way (i.e. 400 billion) to get the probability of any star colliding with any other? Also, the simplifying assumption of using the sun's orbital velocity seems off to me. Wouldn't the more relevant velocity be the collision velocity? That's not a -lot- higher, but it's something like half an order of magnitude, isn't it?

[@jasonpatterson8091]

This was my thought as well. If the initial calculation is the expected number of collisions for the Sun over the course of the merger (roughly one billionth, volume vs cross sectional density notwithstanding) then wouldn't you expect roughly 400 collisions for the merger?

[@nigelm5777]

I couldn’t see what the orbital speed has to do with this problem. Isn’t it the closing speed between the two systems?

[@ianstradian]

Loved this video. Showing the math in simple terms is fantastic, especially since you did it well and treated us mere mortals like we could actually think. I hope to see more of this stuff. BTW: question... Can you please break down the math of the Fermi paradox?

[@Alexis-hx3yd]

I have wondered this for years ,with Andromeda and the Milky Way heading each other’s way, thanks for the heads up.

[@dougsholly9323]

Interesting thought experiment, and my criticism isn't meant to slight her at all, but the 'simplifying' removes the 2 biggest factors when trying to consider collision probability. And when I say 'biggest', I mean to a factor which will drastically changes the results, making whatever numbers she comes up with completely meaningless. But, as a way to reinforce the point of the massive amount of empty space there exists in the universe, it is definitely interesting.

[@thomasdalton1508]

I may be missing something, but why did you divide by the number of stars in Andromeda? That gave you the probability of a particular star in the Milky Way hitting a particular star in Andromeda. What you wanted is the probability of a particular star in the Milky Way hitting any star in Andromeda. Since the probability of a star hitting two stars is negligible, the probability of a collision is approximately equal to the expected number of collisions. That is what you then need to plug into the binomial formula.

[@Carisus]

It sounds to me a lot like the Birthday Paradox/Problem. The chances of our star hitting another star is different from the chances of a star hitting another star. @Dr. Becky did all of the math correct, it was just for the wrong problem. I believe Matt Parker has a stand up routine about this.

[@Kris_M]

@Thomas I was thinking the same thing ("Since the probability of a star hitting two stars is negligible, the probability of a collision is approximately equal to the expected number of collisions.") Then the probability of any one Milky Way star hitting any one Andromeda star is that Z times the number of stars. The title of the video could be interpreted either way though, either "probability of any collision over all stars" or "probability of a specific star hitting another specific star".

[@helgefan8994]

Yeah that division by the number of stars in Andromeda is also what I have trouble with. I considered using an unrealistically dense Andromeda galaxy with 100 stars, and an expected number of collisions of 10 (instead of 10^-9), maybe because the sun also has an unrealistically big radius. What would dividing by 100 now mean? I don't think the probability for our sun hitting any star in this hypothetical Andromeda galaxy is suddenly 0.1 is it? Becky's explanation with the dice (to justify the division) didn't make much sense to me either, considering the different numbers of collisions have vastly different probabilities unlike the 6 equal sides of fair dice.

[@dnomyarnostaw]

Nah. She covered ALL stars in the Milky way hitting ANY stars in Andromeda - goto 11:41 and watch for .00000004%

[@Kris_M]

I don't think so. She set p to be the prob of a specific MW star hitting a specific A star. Then putting it in the equation with n = 400b gives the prob of at least one MW star hitting a specific A star. Still not any A star. I think Z should've been used as p in the bi.distr. (as the OP stated)

[@justpaulo]

Statistics: Mastered ! Camera Focus: still needs improvement ... :) Thanks for this mathy video.

[@ShainAndrews]

Focus... I seriously thought my eyes were deteriorating faster than I thought as I just got glasses for the first time.

[@Animaniac-vd5st]

I just love listening to her. A woman of serious intelect talking with such enthusiasm about sciency stuff alone does something for me, but her voice and facial expressions just makes it perfect.

[@vikingsoftpaw]

My sentiments exactly. Women with her intellect are very rare indeed. Stem girls rule.

[@scotthammond3230]

Star collisions are not so interesting as near misses. Maybe Oort cloud or even Kuiper belt misses. How often, and would that significantly disrupt the planetary systems around the stars? Could you see evidence of this by finding elliptical orbits of planets rather than near circular orbits?

[@Khether0001]

But in the other hand the chance for a body to be gravitationally affected by another body in such merging would tend to 100%, right? This is why the simulations show a complete deformation and directional change of both... Could we calculate that somehow?

[@mikhailman]

These effects calculations were used to create the simulations that we see in the video, together with photo material. I think the collision will bring numerous problems to stars in close proximity to diffuse gas nebolas, which will be thrown around during the collision.

[@BillySugger1965]

Okay, a physical stellar collision is highly unlikely, but there are other scenarios which could be damaging to habitable worlds. Namely, an encounter close enough that a planetary system could be gravitationally disrupted. What does the probability look like if the radius of interaction of not twice the radius of the sun, but twice the radius of Neptune’s orbit instead? Could you do a quick addendum on this please?

[@jamesdriscoll9405]

OK, not many collisions. Quite a few perturbations, by the looks of it. What are the odds of getting ejected from the "fur ball" or captured to the central core?

[@deeparoyal7349]

Yeah, and how's that going to work out for good old stablized life-harboring solar systems like our own.

[@mikicerise6250]

Oh don't worry about that. The sun will be a red giant by then anyway. If we haven't figured it out by then, we never will. ;)

[@rationalmartian]

Would it really matter? As long as it isn't the incredibly unfortunate collision. The solar system itself should really remain intact, certainly the inner parts of it, including say Mars and maybe the asteroid belt. The vast majority of people have no idea what is in the sky even on a trivial level let alone the solar system or further afield. As long as they still see the moon, I doubt many people would even be aware anything had happened. You can also rest fully assured that any media reporting would be laughably asinine, inept and childishly simplistic, dumbed down and hyped up. Quite why or how one could or need to hype something like this up I cannot imagine. But I have confidence they would manage it. Going off past experience. But to be honest, as things stand I doubt the human race will manage another hundred years. I feel our biggest threats come from ourselves. I have become more pessimistic the more I age, and I don't think it is all entirely due to me becoming a miserable, cantankerous, curmudgeon. Though of course I do hope so.

[@jamesdriscoll9405]

@@rationalmartian Well, my money is on anyone around for the show will have the technology to mitigate any discomfort, having survived worse.

[@pnumekin3642]

@@rationalmartian A bit closer to the sun or a bit further and life lights would be out and that is if the planet isn't trhow in to the sun or pushed out of the system altogether. A Star, even a small one , entering the solar systems would cause a lot of gravitational havoc.

[@chiraldude]

A more interesting (and complex) question would be the odds of a solar system being disrupted by a near miss such that a habitable planet gets kicked out of the habitable zone.

[@BooksandCaffeine]

"Statistics ... everybody's least favorite topic in Math" (Head drops, looks dejected) "Umm, I'm a PhD student in Probability. It isn't my least favorite topic." Astrophysicists are mean. :(

[@LordDragon1965]

Couple questions: 1. I presume the "lesser collision" would be as if Milky Way sucked up one of the Magellanic Clouds, right? 2. Wouldn't the likelihood of collision be significantly higher closer to the core black hole and/or at the point in the spiral arm that is between the two black holes? 3. Have we seen an actual stellar collision while observing galactic collisions or would we know if we had?

[@larsenc84]

TL;DR collisions are several orders more common than she describes (under ideal conditions), but still quite a rare event. This explanation doesn't really take into account the angle of impact, the relative velocities involved, or the respective direction of rotation for two colliding galaxies. If the galaxies come together neatly, rotating at a similar velocity, along the same plane and direction of rotation...then the slower relative velocity of these two bodies would allow gravity between the stars to do a lot of the work, increasing probability of a collision greatly. The cylinder analogy seems an oversimplication. Keep in mind Dr Becky is assuming only one pass through the galaxy, when in truth there will be many galactic orbits involved Her estimate of average star mass was a bit high. 90% of stars out there are red dwarfs, much smaller than our Sun.

[@fredericdewitt1208]

Amazing when dealing with that many stars. Think of this! 52 (# of playing cards in a deck) factorial=8.0658x10 (67). That number is larger in seconds than the universe is old! The odds of shuffling a deck and that exact order of cards has appeared before is unbelievably small. The odds of you winning the lottery five weeks in a row are much better than shuffling a deck of cards that has appeared before in all of history. I love numbers, and your productions. You make my days.

[@VernAfterReading]

Wonder how that changes if instead of collisions, we look for likelihood of a star coming close enough to the Ort cloud to send a shower of comets into us. The Ort cloud radius is like 20-50k AU, so much bigger.

[@BIGV1N]

Or even another stars Ort cloud crossing paths with ours....

[@williambrandondavis6897]

If a star came close to such small objects like asteroids its massive gravity would suck them into it. If another star got any where near our solar system to effect it gravitationally, asteroids would be one grain of a sand in a bucket full of things we would need to worry about. We would be goners.

[@andrewr499]

I really enjoy your videos, but unfortunately there is an error in calculating the final probability. p has no dependence on NA because Z is proportional to NA, and p = Z/NA. How can the probability of *any* collision not depend on the number of stars in Andromeda?

[@henryD9363]

Her math is terrible. It states that the more stars there are an Andromeda the less likely a collision exist. Crazy

[@DavidAspden]

Outtake gold! Very enjoyable video.

[@markdodd1152]

This is so cool that you made a video about this. As I was watching your Saturn video during the animation of the black hole my first thought was I wonder if stars ever collide

[@randybrisendine2043]

Love the channel! Personally, I appreciate everything you do! Thank you! I also love the accent!

[@t71024]

What is the probability of a "near miss" close enough to disrupt planetary orbits?

[@mark2073]

What are the chances that the 2 galaxies would even collide? The same analysis could be done for galaxies colliding, not stars. Gravity plays a big role in pulling things together.

[@watong9232]

Having just recently read about the Andromeda / MW merger a week or two ago, I was wondering this very same thing! Fascinating! Thank you!

[@marc-andrebrunet5386]

🎯Space is so big, and each time I think about that, it blows my mind, again and again..🎇

[@quackpackactual]

Cool video! Subscribed. Funny thing about stats: I bet that at least one star would collide in an actual merger because tiny, tiny odds do happen in real life. Calculate the odds that one bullet fired in the Civil War would hit another bullet mid air and fuse...well, we have several examples of that. Reminds me of the old joke about how many cows could fit in any given area, and the mathematician says: Assume a perfectly spherical cow... Not to belittle your math, but existence is so much more special than statistics could ever represent.

[@erikthedragongeek7657]

Came for the science stayed for the bloopers..brilliant! Lol

[@thomass.586]

Very interesting, I especially like your little GoT-performance at the end. What I would like to know is if it is inevitable that the supermassive black holes of both galaxies merge eventually and what the implications of that would be for the newly formed galaxy. Black holes with the mass of millions of suns colliding would certainly mean a titanic explosion, affecting everything within a radius of thousands of light years I would imagine.

[@lordchickenhawk]

Cody's lab did an excellent demonstration of the vast amounts of empty inside the galaxy by making a scale model of the solar system on an American football field. With a pea representing the sun, and a poppy seed for Jupiter (about four meters away)and so on. Then he got a 3 more seeds to represent the Alpha Centauri system and left the stadium so as to place them according to the same scale... then he left town... then the state. 202Km away he got out of his car and placed a radish seed by the side of the road... representing Proxima Centauri, our nearest stellar neighbor. It's a good video, I'll post a link if anyone wants it. That video made it clear to me how galaxies could collide without any stars running into each other.

[@Stadtpark90]

lordchickenhawk Thanks. Looked it up. Here you go: kzbin.info/www/bejne/mnS2eouCft-bsM0

[@unkelpipit7157]

Yup. Saw that video too. The distance is truly mind boggling.

[@differous01]

So, for an English comparison, the distance between the sun and its nearest neighbour is like a pea in Old Trafford (Manchester United FC), and a radish seed in St. Giles', Oxford (famed for its inklings).

[@BIGV1N]

That video made my brain hurt lol, in a good way though. I love CodysLab!

[@BillPalmer]

Another analogy I heard was if the sun was the size of a grain of salt, the nearest star would be 4 miles away. And that’s why there are no aliens here.

[@dimitriskaraiskos8559]

I've watched a lot of your videos,but this one made me fall for you!!! Bravo!!!

[@moviemaker2011z]

2:00 wait a minute, did you just say milkymay?

[@artjackson8360]

I'm so glad to finally hear a astrophysicist using the phrase "galactic merger" instead of "galactic collision" when talking about this subject. It's always bugged me when they say "collision" when almost nothing actually hits each other.

[@ricktollefson6077]

Next question: What is the behaviour of the two central black holes when their galaxies collide...?

[@RichMitch]

Same thing, merge

[@atimholt]

This is where supermassive black holes come from. There’s an upper limit to the size you can get from just a supernova. If there’s any exception to “negligible gravity” approximation, black holes are it.

[@giles4565]

@@RichMitch Is it possible that the two black holes could sling shot off each other rather than merge? I guess it depends on the relative mass of the two black holes?

[@epoch80]

Are you using a small depth of field on your camera lens? It seems you can have your face or your certificate in focus, but not both. Change your aperture (if possible), and therefore depth of field and it will all be in focus. Consider some foam sound absorption panels on walls to further improve acoustics also. Great videos none the less.

[@janernn]

Snapchats of what's going at any different stage in the merger

[@jamessharier7529]

Wow, your math is simply elegant and so was your presentation of the probability.Love how you present it so logical and informative. Glad I stumbled upon this.

[@Darkswordz]

"ShapChot" = Interstellar Social Media.

[@Fudmottin]

@Pronto So not much different from Twitter then.

[@supremeownage8995]

Another wonderful video. I have a question. You described the paths the suns would take as a cylinder through space. What sort of size would be required for a sun to come close enough to another sun to disrupt all the things that are in orbit? I've always imagined our merger to be along those lines, with all the overlappying suns wizzing around with all their gravitational influences, wouldn't all the things in orbit just get flung off into the void?

[@AvangionQ]

Change the radius to Saturn's orbit ... any star getting that close will do damage, even without a direct collision.

[@cperez1263]

I love this video! You remind me of a one of my favorite teachers from my youth. Well done.

[@horstherbert35]

A more accurate (and earth-relevant) question would be "what's the probability that there will be a gravitational interaction with another star" Because if you only account for direct collisions, there's just too many possibilities unaccounted for.

[@BillPalmer]

Jim Panse exactly. If another star comes swinging by the Ort cloud, planetary orbits will be disturbed- might not be pretty after that.

[@christopherconwell7271]

Love how you explain such Technical Knowledge so as we can all understand it. Or maybe at least some of us. 🤯 All kidding aside . I just subscribed the other day and I'm already hooked on Astrophysics..

[@inerlogic]

tl;dr = really small, space is full of space. #SnapChot

[@milkdrinker7]

What about the chance of stars coming close enough to disfigure the solar systems?

[@xCorvus7x]

11:03 Shouldn't that be (1 - p)^(n-k)?

[@AndDiracisHisProphet]

yes. it also should be (n-k)! in the denominator of the binomial coefficient.

[@irrelevant_noob]

... in fact, i think there were even more mathematical faux-passes in the video, when it comes to the nitty-gritty of the statistics involved: * why divide Z by NA? o.O * why go for "exactly 1 hit" as opposed to "at least 1 hit"? -.- Maybe more, but my own grasp has gotten rusty over the years.

[@TechNed]

Dr Becky, I think you blew my mind with (400 billion)! My trusty Corvus 500 craps out at factorial 120 (which is still 10¹⁰⁰ times greater than other calculators of its era) but "astronomical" almost doesn't seem like a strong enough word to describe it. Luckily the denominator quells things but if ever there was a case for execution of the HCF command (Halt and Catch Fire), I'm looking at it..

[@NicholasA231]

Holy crap! Is that really what it said?! My math skills aren't that great, so my internal voice(s) had a quick discussion, decided I was just missing something, and glossed over it. As in - "Wait, why is there a ! *there*?" "Remember statistics?" "Yeah, but..." "Right... Obviously she's doing something you're not familiar with, and that ! means something different in this context." "Okay, that's a relief, carrying on".

[@TechNed]

@@NicholasA231 I know what you mean. Mine aren't either and I do that a lot but factorials pop up in many probability equations. I had to do a double take just to remind myself that n!/(n-1)! = n.

[@user-nn6sw6ey8j]

Probably need to update your info on the mass comparison of the milky way and andromeda...milkyway is now considered at least as massive if not more massive ...

[@culwin]

Why did you use 2r of the sun? Shouldn't it be 2d (that looks like what you drew)? 2r is just the diameter of the sun... And anyways shouldn't it be 3d, since it could just touch the sun at the top, or the bottom, or right in the middle?

[@Riker626]

Whats the probability of a passing star pulling a planet out of orbit?

[@whykoks]

Probability of spotting aliens

[@halfhouse5760]

Well done, Dr Becky! We appreciate your detailed explanation of the reasoning you used to arrive at the probabilities asked in the question. It reminded me of a good university lecture. :-)

[@qerfqbAZRE]

You answered a question I probably asked to my father thirty years ago 😀

[@jayablejay]

Dr. Becky, thanks for taking the time to post this video. I live in the Atlanta Ga area and I to better visualize this probability i shrunk the sun do to the size of a golf ball. From Atlanta the nearest star to our golf ball size sun would be in Dallas Texas. Using the same proportions, I cannot begin to guess how far the most distance star in the Milky way is from the sun. But it demonstrates how vast the space is between stars and how very unlikely a collision between two galaxies would result is stars colliding.

[@ericgulseth74]

This reminds me of a cosmic sized Rutherford Gold foil experiment.

[@ericgulseth74]

@@GeeBee135 Wasn't he firing alpha particles, not neutrons?

[@meteoman7958]

I have actually wondered about that. Now I can relax, thanks. Belated Happy Birthday.

[@kurtfitzner1290]

When simplifying the way this video suggests (no gravity, our sun is median star size) then it has nothing to do with volume and everything to do with cross-sectional-area. It becomes a two-dimensional problem. You flatten the two galaxies along their axes of travel as if you are projecting them onto screens and then bring the screens together. Thus the real considerations are the cross-sectional area of each star (2.Pi.R) times the number of stars compared to the total cross sectional area of the galaxy. This gives you the flattened density and, essentially, the odds of hitting anything. One very important thing left out of the simplification entirely is the angle the galaxies collide at. This strongly affects the flattened density. If they hit edge on, there will almost certainly be huge number of star collisions. Imagine projecting a galaxy edge on onto a screen - do you expect there will be much empty space? The second way this video's simplification strongly fails to approach reality is it's removal of rotational speed from the equation. The faster galaxies rotate (compared to their lateral motion) strongly affects the odds. This is where you have to take into account 3D effects. Try throwing a pea-sized rock through bike spokes when it's still and when it's spinning fast and this illustrates the issue. This is also something that will act to greatly increase collisions and increase them even more the more they collide edge on. In short, the math is wrong, even with the right math the math didn't take into account the density difference taken by the angle of attack, and finally, the simplification failed to take into account a factor that works to greatly increase collisions.

[@OrbitTheSun]

The error occurs at 9:32 when she divides by N. Instead it should be multiplied by N.

[@petehiggins33]

I would suggest that Dr.Becky has cleverly avoided all the problems that you have highlighted by assuming that instead of a single collision, there is a continuous series of collisions lasting for a billion years and the speed of the collisions is the initial rotational speed of the galaxies (as mentioned at 8:34). This way all she need to know is the volume of the galaxies and density of the stars and doesn't need to know anything about their shape or angle of attack which would be really complex to take into account.

[@Fam2014Ch]

WOOOOW... one of the most interesting videos I've ever watch !!! Thanks AGAIN Dr B !!! ... happy to learn something else today !!! Thanks !!!

[@robertgoss4842]

I am a senior citizen, happily married for decades, but I'm pretty sure I'm in love with Dr. Becky. Thank you and good night.

[@skakofilsanonims4434]

Good start. Would be good taking into account that collisions can go through all directions locally, and an algorythm of calculating the chain effects of two stars colliding, and the effect of the gravitational variation as the galaxies approach, etc.

[@calinculianu]

The little plant on your desk is in focus. You are not. :)

[@pgantioch43]

Somehow I have a feeling that the probability that Oort cloud disruption (ours & those of other stars, presuming they exist) by gravitational interactions will be significantly higher. So we could have a LOT of impacts. There also will be a burst of star formation, & some of them will be large enough to go supernova, with the attendant risks.

[@giles4565]

I would assume if another sun went even within the radius of our solar system that would be enough to pull earth off its normal orbit significantly. The question of what is the probability that the collision wipes out life on earth I suppose is really the more pertinent question.

[@mikicerise6250]

We don't have to collide though for a close flyby to seriously ruin our day. ;)

[@CarFreeSegnitz]

Yup. A solar mass that passes our sun within 10 AU could easily perturb orbits enough to toss the Earth into the sun or tear it away into interstellar space. Just kicking the Earth into a highly eccentric orbit would end habitability.

[@williambrandondavis6897]

@@CarFreeSegnitz Not to mention the possible effects of high radiation from two stars shinning on our planet from different directions.

[@M31glow]

Hey Dr. Becky, how does this relate to LIGO catching the mergers of neutron stars / black holes? How would they have gotten funding if the % chance of collisions is so low? In there press release they predict seeing as many as a 1,000 per year ... I think.

[@brtle]

Simply choosing to "ignore gravity" when producing these statistics is a monumentally egregious over-simplification that renders these numbers meaningless. Gravity is the _engine_ of this process, and near-misses by stellar-mass objects can easily be _as_ disruptive as a "direct hit". Also, as stars themselves are not "solid" objects, but rather are simply gravitationally-bound blobs of plasma, what does "hit" even mean in this context? Wouldn't they simply pass through each other following essentially the same particulate rules ( subject to _gravity!_ ) that you're applying here to galaxies, but just on a molecular scale instead? In any case, for the purpose of pondering the future of our Solar System with regard to our theoretical perspective (whereby, if we manage to make it so far, we'll no longer be living on a then-uninhabitable Earth anyway), the disruptive gravitational effects of even "near"-misses by multi-Solar-mass objects easily represents the greatest threat to the integrity of our local planetary neighbourhood as compared to the miniscule probability of an actual direct stellar-collision, but you discarded this factor at the outset! A ~5-SM white dwarf, passing inside 1000AU of Sol, could destroy our solar system just as effectively... What happens to the odds of solar-system's-survival when the diameter of your cylinder is adjusted accordingly and such considerations are then factored in? Now _THAT_ would be a meaningful exercise! 🤔😳

[@xl000]

can you tell me where you got your PhD ?

[@brtle]

@@xl000 -- first, take a few minutes to go look up the following: Argument from Authority Fallacy Ad Hominem Fallacy Poisoning the Well Fallacy (Note: you're only committing _ONE_ of those here, but can you figure out _WHICH_ one? 🤔) As any student of basic epistemology knows, facts stand or fall _on their merits_ and not upon the credentials of the person espousing them. If you want to challenge my arguments *_on their merits_* by all means, please feel free to do so! I'd be happy to address them. But to witlessly ask such an utterly meaningless question as you've done here, ostensibly in the naïve belief that it has any bearing to the argument itself, _only_ actually demonstrates your own intellectual insufficiency to the job.

[@gg5115]

While not disagreeing with any particular point, the Sun is by far the most solid object in the solar system. And it's plasma. Metallic plasma. And once you get below the surface, far denser than the core of any planet. Hard to wrap your head around that much gravity.

[@brandonshebester9574]

The world needs more of you. Gorgeous, intelligent and funny! Love the accent too! Maybe you can clear something up for me. The big bang happened. Everything speeds away from a central point. How can major collisions occur? How can anything be on a collision path at this point? Shouldn't we at most be speeding alongside other systems?

[@DrBecky]

Because gravity over comes the expansion on smaller scales. Andromeda and the Milky Way will one day collide for example, because the gravitational attraction between the two wins out over the expansion

[@azraelblick4117]

I'm in love with a lady over the internet. What is the science behind such phenomena?

[@johanveltheim4331]

Would be unbelievably cool to see such a collision though! (And besides, don't one in a million chance things happen all the time?) It's different to neutron star/black hole collisions in that you could actually be watching it (for a while at least until the resulting trainwreck squirts something unpleasent at you) with your own eyes on a nearby planet (using suitable eye protection... and probably in an air conditioned room but still). Dr. Becky should do a quick simulation on what it would look like!

[@zerg9523]

Who’s watching this in 2000002019?

[@jonathanlindsey463]

Zerg which will still be 2 billion years before Andromeda catches up to us in our race towards TGA

[@slugfly]

But what are the chances of solar systems being torn apart by passing gravity wells? Same?

[@nehukybis]

Ironically, Jesus Christ on a Crosstrainer is much harder to say than "snapshot"

[@tedbates1236]

Jesus Christ is your only hope. Mocking the Son of God is an arrogant foolish thing to do. Join the fools of the earth who blaspheme the name of the living God is just increasing the fire.

[@johnbennett1465]

I posted another comment where I suggested you do a variation of your calculation. After posting it I decided to try it myself. When I did this I ran into two issues. 1) I looked at your probability calculation and think you are computing the chance of the sun running into a specific star in Andomada. I understood you as presenting it as the probability of any star in the milky way hitting any star in Andromada. 2) I tried to reproduce your calculation before doing my variant. I came up with 1.6e6 for z. I converted all lengths to kilometers and the time to seconds. Is there any other massaging of the values I need to do before pluging them into your formula?

[@gammaraygem]

you are being...ehh...naughty. but then, she was too ignoring gravity, how dare she !

[@johnbennett1465]

@@gammaraygem actually, if you look at my other comment, it is all about the havoc that gravity would wreck with a near miss 😀.

[@Majoofi]

Discount gravity? Gravity is the whole story when galaxies merge.

[@DarkAngel71180]

Majoofi you're talking about the gravitational force of an entire galaxy versus the force of individual stars. She calculated the probability of 2 STARS colliding, not 2 galaxies. The individual stars' gravitational forces are what's being discounted because the space between the stars is too great for any one star to influence another during a merger. I believe that range of gravitational influence is called a Schwarzchild radius? The radius at which gravitational pull ends for any object. I probably butchered that spelling sorry.

[@CarFreeSegnitz]

Devi Schwarzschild radius is the radius at which a given mass becomes a blackhole. There is no such thing as a distance at which a mass ceases to have a gravitational effect. Gravitational effects asymptotically approaches zero but never actually reaches zero.

[@colinjava8447]

I dont think its possible to include gravity, the system becomes chaotic very quickly even if you assume the stars are evenly spread. I think you need a supercomputer simulation to give you realistic odds of collisions occurring.

[@farhanulhasan6191]

Not quite. Hydrodynamics may (and probably do) play a huge role and can decide whether star formation or AGN turn on , which in turn decides the fate of the galaxies.

[@NeilThompson]

Question - de simplifying one of your assumptions, what effect would pushing one of the larger, denser Milky Way globular clusters through the plane of Andromeda have on the probability of a collision? Your cylinder becomes larger than the average distance between stars then, doesn't it?

[@MartyWoodcock]

I'm going to borrow "Jesus Christ on a Crosstrainer". Love it.

[@Yesica1993]

Sad to see the name of Jesus used so flippantly, when He is the one who created all these wonders.

[@TheTeufelhunden68]

@@Yesica1993 And exactly what did he create? Since you're on this site, I will assume that you love logic as much as I do. Okay, let's use logic shall we. I shall use the same logical arguments for two scenarios which will show them to be either mutually inclusive, or mutually exclusive, but they can't be both, nor one of each. The 'bible" is an end upon itself. There is no other knowledge of the "bible" than what is written *in* the "bible". Sure, books have been about the "bible" but the source material is the "bible itself". People, such as your Pastor, Priest, Rabbi what have you, may attempt to interpret the "bible", but that's one persons view and highly speculative, barring the many machinations of the individual in question. These statements are obviously irrefutable. Now, let's proceed. This is all very basic, and most telling. The "bible" itself is it's own utmost authority off itself. It is a self referring work. Since no individual or collective members of the Trinity are openly preaching themselves on every street corner, which presumably, being omnipotent, they could, we *must* take the "bible" as it's own authority. So, the "bible" is the TRUTH, because the "bible" *says* that it is the TRUTH. Okay, so far so good. Let's use the *exact* same logic on another scenario. I am the King of England, because I say that I am the King of England. Using these two statements with the same logic applied to each, they must both be true, or they must both be wrong. They can't be both be true, (unless, of course, Schroedinger puts them in a box with a cat, a Geiger counter and a flask of Prussic acid). So which is it? Are both statements true or false? Pssst: A little hint. I'm not the King of England.

[@TheTeufelhunden68]

@@prassel6189 That's not the truly sad part. What is really sad, is that they feel so bad about themselves and have such a low self esteem, that they have to make up supra parental figures couched in superstition and (so their thinking goes) immune to attack as they can't face reality. On a side note, I once lived in a small town in Indiana. I used to see barns that had the phrase "Jesus Saves" emblazoned on the sides. This always got me to thinking about what it is that Jesus actually saves. Bit's of string perhaps. Old tinfoil to make a hat. Maybe old newspapers and magazines for the Cub Scouts. The possibilities are endless. Cheers

[@rufusleekin3482]

@@TheTeufelhunden68 I love science...always have. I'm 60 years old now. Christians (and I mean REAL Christians who have had a real undeniable experience with God) are so misunderstood. We are thought of as backward and irrational people who just blindly believe in fairy tails. To start with, I think most Christians have had educations which included some Science and that when we were young and most impressionable. I don't believe the reverse is true. So what is it that makes someone who is indoctrinated by an educational system which does everything in it's power to dissuade them in a belief in God, become a Christian? Some will say that they have been indoctrinated since childhood by parents. That may be true in some cases but what about all the people who had no church upbringing who suddenly start believing in God? You know that to profess Jesus as Lord comes at no small price if one is going to truly try to live out that faith. We are so often accused as trying to run other peoples' lives and judge them. Jesus himself said to take up our crosses daily and follow Him. If anyone can say there is no persecution of Christians, just look at these comments on this site. It would be a lot easier to just go along with the world and not rock the boat. What about the Christian converts with PHDs in the fields of science, mathematics etc. some of whom have extremely high IQ's Jesus Himself said that salvation by grace seemed illogical. If you have an open mind and give the Bible an honest chance you might see what has been in front of you the whole time. You see, a person with real scientific curiosity would try to answer why so many people would completely give up careers, friends, and their way of life to follow a God for which there is no evidence. Christians are often cited as the biggest ill of society. I think most people who say that have no first hand experience with real Christians. I think they are the ones who have been indoctrinated. I hear how much evil has been brought upon the world by Christians when any thinking person would consider that maybe that is the way the enemy of Christianity wanted it. Christians know something that non-believers don't. We have heard the other side and many of us were on that other side. Nothing short of a miracle would have changed us. You see, for me it is not just blind faith, but a still, quite voice which drew me to Christ and which now lives within me. You can't find that with logic or science. But once you know the truth and start to put God as the foundation of creation and then study science from that perspective then so many truths start to open up. There is nothing wrong with science, but thousands of years ago the bible warned to avoid the profane babblings of the "men of science so called". Come on folks; If the Mars rover took a picture of a Nike shoe box on the Martian surface today, you would say it was undeniable proof that some higher intelligence had created it. Yet when you see the complexity of DNA, you say it just happened naturally, or even that an advanced alien civilization created it. People would rather believe in aliens than God. Just remember, all you people who believe that no rational person could believe in God, that of the giants of science past such as Newton, Galileo, Kepler and so on believed in God. Maybe you don't feel a need for a God now, but once you meet Him for real, you won't know how you could have been so blind. As for all those Christians who encourage you to go to Church.....cut 'em some slack. Try not to look at it as if they are butting into your business. Try to see them as someone who has found a cave full of treasure so vast they can't possibly carry it all and they just want to share it with you.

[@bobbymcgee723]

I was on-board with this topic, until you glossed over the idea of one star from galaxy(a) passing thru the vicinity of a start from galaxy(b).(a being Andromeda and b being the Milky Way.) Yes, stipulating a DIRECT collision makes the math easier... and thus more amenable to a KZbin video... But the idea of any object, be it star or otherwise, passing anywhere near (or thru) our solar system and not wreaking complete havoc, is crazy.

[@KyrosX27]

Love the outtakes in the end! (Brought to you by the _Snapchot_ team)

[@yolafur]

Dr. Becky. What are the odds that solarsystem collide? In other words, what are the odds that the gravitational fields of the incoming systems disrupt one way or the other, the existing systems? Maybe throwing planets around and or altering the orbit of a system around the galaxies center.

[@koenth2359]

If you were to traverse the disc of the Andromeda nebula at right angles, what is the probability to hit a star? A very simple calculation: Radius of Andromeda disk: R=1.1E5 ly=3.5 ×10^12 light seconds Radius of a typical star, like sun 690000 km=2.3 light seconds Number of stars in Andromeda n=10^12 The probability to hit some star is the fraction of the area of the disk that contains a star, which is nr^2/R^2=4.3×10^-13 For a particular star of the size of the sun to hit any star of Andromeda, we'd have a collision whenever the stars pass at less than 2r, so I get a probability of 4 times that number, about 1.7×10^-12 And since the Milky Way contains about 2.5×10^11 stars, I'd say the chance for any collision is about 40%. So I do not see where 10^-19 comes from (and the probability will only increase if you traverse it at an angle).

[@whutulukinat]

If there's already a video of this question, please point me in the right direction. But what would be the result of 2 stars similar to ours colliding? Do they merge and make a larger star, or maybe explode/implode because of the violent collision? Thank you Dr. Becky, I love the way you explain these things although I am pretty much mathematically illiterate. Lol

[@BreakingBarriers2DIY]

I'm ok with confining the calculation to "our sun's conditions" of size...proximity to other stars...etc. I'm a bit more selfishly interested in that.

[@thelastneanderthal3171]

Dr Becky, you made my head hurt with the mathematics, but I got it. I won’t loose any sleep over it. Thank you.